In　this　paper,　a　novel　kernel　adaptive　filter,　based　on　the　least　mean　absolute　third　(LMAT)　loss　function,　is　proposed　for　time　series　prediction　in　various　noise　environments.　Combining　the　benefits　of　the　kernel　method　and　the　LMAT　loss　function,　the　proposed　KLMAT　algorithm　performs　robustly　against　noises　with　different　probability　densities.　However,　an　important　limitation　of　the　KLMAT　algorithm　is　a　trade-off　between　the　convergence　rate　and　steady-state　prediction　error　imposed　by　the　selection　of　a　certain　value　for　the　learning　rate.　Therefore,　a　variable　learning　rate　version　(VLR-KLMAT　algorithm)　is　also　proposed　based　on　a　Lorentzian　function.　We　analyze　the　stability　and　convergence　behavior　of　the　KLMAT　algorithm　and　derive　a　sufficient　condition　to　predict　its　learning　rate　behavior.　Moreover,　a　kernel　recursive　extension　of　the　KLMAT　algorithm　is　further　proposed　for　performance　improvement.　Simulation　results　in　the　context　of　time　series　prediction　verify　the　effectiveness　of　the　proposed　algorithms.